Basilisk is lite mode. You do not download the blockchain, but simply connect to notary nodes.
Basilisk is a mode similar to a "Lite" mode but with several important key differences. Traditional Lite Clients connect to a CENTRAL SERVER and execute transactions FROM THAT SERVER.
Basilisk mode connects to ELIGIBLE IGUANA FULL NODES and sign transactions LOCALLY.
These key differences mean that unlike traditional lite clients your coin is still kept on your system.
Thank you guys for the fast replies. I think I'll be going with Basilisk for the time being especially since I'm going to install it on Windows and that there seem to be syncing issues:
Apparently there is some bug on windows when using full mode, but according to yassin the Basilisk mode works nicely.
If on windows, basilisk mode should be used, there are some sync issues still in full mode on windows.